Barack Obama’s re-election effort once looked to be a tug-of-war between two powerful political forces: the magnetism of a charismatic incumbent vs. the drain of a slow economic recovery. But a month before Election Day, the President’s charisma went missing, at least for one debate night, while new jobs numbers suggest that the economy isn’t such a disadvantage for Obama.

The headline of the government’s monthly jobs report released Friday was that the economy added 114,000 jobs in September, while the unemployment rate fell to 7.8%. That’s not all that great: the jobs total barely keeps pace with population growth, and near-8% unemployment is far from ideal. But read into the report — and between its lines — and the news should be heartening for Democrats spooked by their candidate’s poor debate performance Wednesday.

Large upward revisions to the jobs numbers from July and August, reflecting a total of 86,000 more jobs than initially estimated, suggest that the summer slowdown that had some observers crying stagnation was merely noise in the data. (They’re also a helpful reminder that economists’ predictions about jobs and growth have a large, but rarely mentioned, margin of error.) The trend over the past year has been a plodding march toward recovery, frustratingly slow but moving in the right direction. The drop in the unemployment rate in September was not caused by a shrinking labor force, by people giving up on finding jobs. Instead it was accompanied by a significant influx and 873,000 new people who said they were employed. Government employment, which nearly every report claimed was recently bleeding, actually increased by 10,000.

The political impact of such trivia from the Bureau of Labor Statistics shouldn’t be overstated. The state of the economy is largely baked into Obama’s re-election numbers at this point; a yearlong trend of modest recovery continues to favor the incumbent. And the most potentially important economic event every month is the one that still hasn’t happened: a sudden financial crash, instigated by Europe or something else, that could pull the presidential race from its moors. The number that the political press will obsess over is the unemployment rate. “No American President since Franklin Delano Roosevelt has won a second term in office when the unemployment rate on Election Day topped 7.2%,” goes the line in thousands of articles every month. But political-science research suggests this number doesn’t matter; the trend is more important than any absolute figure.

That said, the media’s obsession with the unemployment rate can have its own effect. Positive headlines (like this one) can affect voters’ views of the economy and the President. The 7.8% figure is especially likely to generate positive press, for mostly arbitrary reasons: it’s below the 8% mark under which Obama’s transition team infamously predicted the stimulus would keep the unemployment rate. It also happens to be a single tenth of a percent below the unemployment rate during the month Obama took office, robbing Republicans of some of their most biting economic talking points.

This symbolic significance has led some conservatives — including no less than business luminary Jack Welch — to accuse the Bureau of Labor Statistics of cooking the books. The charge is absurd, and it says more about the frustrations of a Republican Party that was convinced for months that the economy would be Obama’s downfall than it does about the BLS’s bulletproof credibility. Mitt Romney is left with a tricky case to make. “We created fewer jobs in September than in August, and fewer jobs in August than in July,” he said Friday, in a nifty piece of spin. “This is not what a real recovery looks like.” But the penultimate monthly jobs report before the election — the last one that will have a chance to influence many voters — is harder to debate than Obama.